That's no different than having a +2 bonus, or a +6 or whatever - you're unlikely to fail easy checks, and more likely to succeed at hard ones. And since being an expert is a persistent condition, it doesn't make sense to lump it in with the same mechanic used to model temporary circumstantial variables.
Except that it (arguably) messes up the math. As we've seen in this thread, some people consider the infallible rogue who trivializes certain challenges to be a feature rather than a bug. So, while they could have decided to use Advantage as the expertise mechanic, if they wanted to "solve" that bug, there would have been just as many people complaining about it either way. So they erred on the side of consistency, and letting rogues have something nice for once.
It is a pretty large difference. A straight + doesn't quite have the same effect as advantage, and also increase the top DC that can be reached. It also interacts with reliable talent to increase the floor for the roll. Advantage has a big effect for low d20 rolls, but less for high ones. A straight + is a flat effect.
And advantage doesn't mess up the math, it uses different math. And, at at 9th level, with a max stat, your RAW expertise is +13 to that skill (+5 stat, +4 prof, +4 expertise), my method is +9 with advantage. Both can't fail DC 10, your fails DC 15 5% of the time (on a 1), and mine fails 6.25% of the time. Pretty much the same. On DC 20 checks, RAW fails 30% of the time, mine 25% of the time -- my way is better. At DC 25, RAW fails 55%, mine 56.25% of the time -- we've closed the arc. Essentially, my method provided better results at this level for DCs between 16 and 24 than RAW does. You do have a better chance of success at DC 30 checks, as via RAW you can hit that on 17+ but it's impossible for a +9, but I'm more than okay for leaving legendary skill checks for higher than Tier II. YMMV.
Until you run the math, you're likely to misrepresent the impact. My method actually improves chances of success for medium to hard checks while leaving easy checks mostly alone. What it doesn't do it add number porn to the dice and amp up ability to well past legendary stats just to make easy tasks reliably beatable. It gets the 'goal' of expertise but skips the distortion of the RAW method.
You are more than welcome to hew to RAW. It's workable, albeit it requires a DM to recognize and change how the game plays to accommodate the ability by changing how she challenges the PCs. Quite often, since this effect isn't called out in the rules and is a bit surprising when it shows up rather stealthily, a DM will make a few bad calls before getting it right, if she ever does. But, still, there's nothing horribly wrong with the RAW. I like 5e well enough that I'm picking on things that are not huge issues because they're stamped out most of the huge issues already. Still, I'd prefer that expertise work a good bit more elegantly within the good system of 5e than just another number plus that distorts the possible to provide protection against failing the mundane. I think expertise does this better than the RAW system. You're not wrong to disagree with me, but I'm also not wrong to disagree with you. We're decidedly in the realm of preference. I would like to point out that if expertise was initially advantage and not double prof bonus, you'd not likely be complaining that it doesn't work as advertised.